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CHAPTER 6 ■ ABSTRACTION 133
search recursively with new limits. You could even make this easier to use by making the limit
specifications optional. You simply add the following conditional to the beginning of the
function definition:
def search(sequence, number, lower=0, upper=None):
if upper is None: upper = len(sequence)-1
...
Now, if you don’t supply the limits, they are set to the first and last positions of the sequence.
Let’s see if this works:
>>> seq = [34, 67, 8, 123, 4, 100, 95]
>>> seq.sort()
>>> seq
[4, 8, 34, 67, 95, 100, 123]
>>> search(seq, 34)
2
>>> search(seq, 100)
5
But why go to all this trouble, you ask? For one thing, you could simply use the list method
index, and if you wanted to implement this yourself, you could just make a loop starting at the
beginning and iterating along until you found the number.
Sure. Using index is just fine. But using a simple loop may be a bit inefficient. Remember I
said you needed seven questions to find one number (or position) among 100? And the loop
obviously needs 100 questions in the worst-case scenario. Big deal, you say. But if the list has
100,000,000,000,000,000,000,000,000,000,000,000 elements, and the same number of questions
with a loop (perhaps a somewhat unrealistic size for a Python list), this sort of thing starts to
matter. Binary search would then need only 117 questions. Pretty efficient, huh?
■Tip There is a standard library module called bisect, which implements binary search very efficiently.
Throwing Functions Around
By now, you are probably used to using functions just like other objects (strings, number,
sequences, and so on) by assigning them to variables, passing them as parameters, and
returning them from other functions. Some programming languages (such as Scheme or LISP)
use functions in this way to accomplish almost everything. Even though you usually don’t rely
that heavily on functions in Python (you usually make your own kinds of objects—more about
that in the next chapter), you can. This section describes a few functions that are useful for this
sort of “functional programming.” These functions are map, filter, reduce, and apply.